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In this paper, compensator dynamics are introduced in sliding mode through a new class of switching surfaces which has the interpretation of linear operators. Two design methods are presented, the first is based on pole placement, whereas the second is based on frequency-shaped quadratic optimal control formulation. The compensators are designed to attenuate the frequency contents of the sliding mode dynamics such that unmodelled dynamics are minimally excited. The design method using frequency shaping is applied to the control of a flexible link robot arm. Simulation results show that the excitation of the link deformations are minimized while preserving the insensitivity of the sliding mode.
Young et al. (Sat,) studied this question.